How do you write the standard form of a line given (2.3) and (4,5)?

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How do you write the standard form of a line given (2.3) and (4,5)?

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Answer 1 · 2016-07-03T17:55:54

The standard form of a straight line is $y = a x + b$ $y=ax+b$ , if the line is not horizontal or vertical.

Explanation:

To determine the standard form of the line we need to find the value of the parameters $a$ $a$ and $b$ $b$ . We know that the line passes through the points $(2, 3)$ $(2,3)$ and $(4, 5)$ $(4,5)$ , so both points satisfy the line equation. That is:

$3 = a 2 + b$ $3=a2+b$ , because of the first point, and
$5 = a 4 + b$ $5=a4+b$ , because of the second point. Then, subtracting the second minus the first, we get:
$2 = 2 a$ $2=2a$ , and so $a = 1$ $a=1$ . Substituting in either equation (say the first one), we get:

$3 = 2 \cdot 1 + b$ $3= 2*1+b$ and so $b = 1$ $b=1$ . The standard form of the straight line is:

$y = 1 x + 1 = x + 1$ $y=1x+1=x+1$

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How do you write the standard form of a line given (2.3) and (4,5)?

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